A hard question. Its possible that Bethesda will do a future DLC that revolves around the CW. There could be aan extra quest if you haven't started it. My Nord Dragonborn Warrior acknowledges both sides of the war. But I guess the question is either to wait or pick a side. But if I do pick a side, which side?

That is a decision your character has to make himself.

The Imperials did little to endear either of my characters to their side when they attempted to decapitate me at the beginning of the game.

Azrael
The Nord with the Sword

If they do I don't think it will be any time soon, and if you do decide to do the Civil War quest and pick the side of the Imperials just make sure you complete it before the Season Unending quest which is part of the MQ or the Civil War quest for the Imperials will break and it won't be possible to finish it.